Formation of curved surfaces of prescribed figure by grinding and/or polishing



Jan. 27, 1948. BURCH 2,435,126

FORMATION OF CURVED SURFACES OF PRESCRIBED FIGURE BY GRINDING AND/OR POLISHING Filed May 8, 1946 2 Sheets-Sheet 1 FIG; 1..

v INVENTOR ATTORNEYS C. R. BURCH FORMATION OF CURVED SURFACES OF PRESCRIBED FIGURE BY GRINDING AND/OR POLISHING Flled May 8, 1946 Jan. 27, 1948.

2 Sheets-Sheet 2 ATTORNEYS Patented Jan. 27 1948 FORMATION OF CURVED SURFACES F PRE- SCRIBED FIGURE BY GRINDING AND/OR POLISHING Cecil Reginald Burch, Clifton, Bristol, England,

assignor to Metropolitan-Vickers Electrical Company Limited, London, England, a company of Great Britain Application May 8, 1946. Serial No. 668,124 In Great Britain March 19, 1945 Section 1, Public Law 690, August 8, 1946 Patent expires March 19, 1965 2 Claims.

This invention relates to the formation, by grinding and/or polishing, of curved surfaces of prescribed figure of revolution, Although notably applicable in the manufacture of aspheric lenses and mirrors composed of plastic or other glass, the invention is capable of wider application.

Hitherto it has been a common practice in forming aspheric surfaces of revolution to use grinding or polishing tools of annular form, the grinding and/ or polishing operations being effected in a series of overlapping zones or annuli. So long as there are enough annular tools available, and provided that a rapid method of testing residual error is available, even very deeply aspieric surfaces can be made in this way albeit with considerable expenditure of time and with the necessity for the continued exercise of intelligence on the part of the workman and of skill in judging how long each individual grinding or polishing operation shall last. If the required asphericity is large, it proves difficult or impracticable in any reasonable time to blend the grinding or polishing operations on the successive zones; and accordingly the resultant surface. though approximating to the desired shape, does so only in a zoned or annularly faceted fashion.

It is also a practice to form an aspheric surface by grinding with a nominally flat grinding tool which is rotated in its own plane and moved by means of a mechanical linkage known to geometry as a negative pedal linkage so that the plane of the tool moves tangentially to the negative pedal curve of a component of the linkagethat is, where said component moves in a circle or straight line, tangentially to a certain conic section which may be elliptical, parab oloidal or one sheet of a hyperboloid of two sheets and so forth. Although this method may possibly have been adopted in the formation of the surfaces in question by polishing, the results cannot be as satisfactory as may be desired since it is characteristic of negative pedal linkage mechanisms that, although involving movement ofa certain straight line or plane tangentially to a certain conic or other negative pedal curve, the actual point of contact moves along the line or plane as well as along the curve-a characteristic rendering such mechanisms unsatisfactory for polishing for the reason that, with each point on the curve there is associated one, and only one. point on the tangent line or plane, and accordingly a fortuitously occurring hard patch on the surface of the polishing pad would come in contact with one zone only and not the whole surface of the work or specimen; it is relatively easy to make a fiat grinding tool substantially flat and slow to wear, but relatively diificult to make a correspondingly uniform polishing tool or pad.

Considering the grinding properties of machines employing negative pedal linkagemechanisms, it is characteristic that the plane of the nominally flat tool is moved tangentially to a certain negative pedal curve-say, a conic-about the axis of which the work is arranged to rotate, and accordingly that curve, and no other. is of necessity generated on the work, assuming that the tool can cut fast enough, or in other words that one does not try to take too big a cut with the machine; with such machines, the desired shape is obtained by what is sometimes called positive generation.

The present invention has for an object to enable the prescribed shape to be approached to any desired degree with the exercise of relatively little intelligent supervision and personal skill and without involving positive generation of the desired shape, with its attendant disadvantages and limitations especially as applied to polishing.

According to the invention, apparatus for enabling the formation, on an object (herein referred to as the specimen) of an aspheric or other curved surface of prescribed figure of revolution, comprises means for mounting the specimen for rotation about a fixed axis, a grinding or polishing surface arranged for resiliently bearing against the surface of the specimen over an effective area of contact which is a mere fractional part of the desired surface of revolution, for example of the order of 5% or less, means for reciprocating said grinding or polishing surface in a general plane through the fixed axis, means for causing the grinding or polishing surface to assume, or at least tend to assume, substantially such orientation about an axis at right angles to the plane of reciprocation at any location in its traverse as it would have for the same location in its traverse in contact with the surface of prescribed figure.

With the grinding or polishing surface adapted to contact the surface of the specimen over a sufficiently small area, and havin positional free-- dom only in the plane of reciprocation, while having its orientation in this plane maintained nominally correct as regards its immediate location on the surface of prescribed figure, it is contemplated that the part of the grinding or polishing surface which is at any time efiective wholly or mainly in removing material from the specimen, will be dependent upon the amount by which the slope of "the part of the specimen against which the grinding or polishing surface bears, differs from the nominal s'l'ope for that part of the surface'o'f prescribed figure.

The effect of this orientation control is that. when the grinding or polishing surface is traversing a, hill on the specimen, that .is an annular zone of excess height on the specimen, the grinding or polishing surface begins to make effective contact with the rising flank of the hill sooner, makes effective contact with the crest of the hill longer and continues to make effective contact with the nether -flank of the hill longer than it would otherwise do in the absence of orientation control. "Correspondingly the grinding or polishing surface Elingers for a shorter time in effective contact with the bottom of a valley than it would in the absence of orientation control. Accordingly there is a greater intrinsic tendency for smoothing the surface of the specimen towards the prescribed shape than would be the case were the grinding or polishing surface not controlled as regards orientation but free to adapt its orientation-to theslope of the part of the specimen with which it is in contact, irrespective of the departure of said slope from the surface of prescribed figure; by reason-of this smoothing tendencyaccording to theinvention the necessity for intelligentsupervision and personal skill in judging the time during which the grinding or polishing surface must Work on various :zones is minimised.

It will be appreciated that, if the size of the rinding or polishing surface is reduced indefinitely, the effect of orientation control is ipso facto reduced, and conversely if the size of said surface is increasedsuflicientlya stage is reached Where the misfit engendered in the surface being ground or polished during the relative movement between'the specimen and the grinding :or pol ishing surface due to the asphericityof the prescribed shape, become serious. Thus there :is an optimum :size of grinding or polishing surface for each stage of the work and the invention contemplates the provision -of a :set of grinding or polishing tools'of various sizes, any 'one of which may be selected for use at any stage of the process.

in ,practising the invention, the grinding or polishing surface :per so may :be provided in any suitable manner, but preferably as a replaceable pad conveniently secured to, or in some cases resiliently-mounted ion: or in, a holder. .For'grinding operations, the pads may =be-of glass or any suchcontrol may be effected through the intermediary ef a rod or bar fastwith the grinding .oripolishing -pad,zor-a holder therefor, so as to partakenf its positional zireedom in :the plane of reciprocation, iand co op'erating cam means affording ea surface or surfaces along which said Ind (01' :bar can 11011. In a preferred form, the rod ,or bar may b fSBCUIEd to the pad, or holder, so as initially-that is ibefore wear sets into extend normally to the tangent plane of contact surface of said pad, the cam means being a cam of profile whichis the evolute of the surface of prescribed figure. With an arrangement providing substantially complete rolling without sliding between the rod and cam surface or surfaces, the cam wear will "be negligible; moreover, if the rod or bar is normal to the surface of the pad, there will be no necessity for the cam means to be displaced relatively -to the pad or its support in order-to compensate for wear on the pad, namely properly to locate the cam with respect to the contact surface of the pad as it becomes worn in service.

The required evolute cam for use in the formation of any surface of prescribed figure may be constructed in any convenient manner. Such cam may conveniently be defined by the law relating the angle made by the tangent with the axis of the specimen and the axial position of the intersection of that tangent with the tangent parallel to the axis; with a multiplicity of such tangents drawn in convenient manner, their envelope will provide the desired cam profile. It will be appreciated that errors in cam shape-although tending to reflect as corresponding errors in the shape formed on the specimen do not pre clude the attainment of the prescribed surface albeit at the costof increased intelligent supervision and local zonal use of a grinding or polishing pad.

The grinding or polishing surface may be biased in the direction for engagement with the specimen by any suitable means, such for example as by'spring means and/or-gravity, capable of ensuring light, and fairly uniform, contact pressure within the limits of positional freedom of the pad in the plane of reciprocation, such as to be substantially unaffected by hills or valleys on the surface which is being formed to thedesired shape.

Conveniently the grinding or polishing pad may lee-mounted, either'directly or throughrspring means, upon a bar or rod-suitably pivoted to a connecting rod, or equivalent linkage, which in turn is pivoted to a. reciprocating member or carriage; a, rod or bar attached to said pivoted supporting bar may then co-operate with evolute-carn means to provide the aforesaid orientation control.

The cam means employed in effecting orientation control of the grinding or polishing pad, may be such that the shape may be distorted, for example'under screw control, as and when required; such distortion may be effected in order that secondary effects, if such are found to affect seriously the nominal shape which tends to be produced on the specimen, may be compensated, or alternatively so that if a prototype has al ready been made, the cam shape maybe adjusted until the contact area or its optical equivalent (which can be observed on polished surfaces by methods akin to autocollimation or by Newtons rings) remains fixed with respect to the grinding .nr polishing pad during the traversing thereof.

Where the profile of the prescribed fs'hapeincludes a point of inflection, the cam means may include two branches appropriately spaced apart so that the normal rod :above referred to :rolls first along one surface and then becomes transferred for rolling along'th'e other surface.

In :an alternative arrangement it is also contemplated that the bar on which the pad is pivotedishould be fast with a bar carrying a pin, or

preferably a roller, engaging with the surface of a cam. This arrangement is more particularly preferred when the speciment is pseudoplane-for example a Schmidt plate (so that were the evolute cam arranged hereinbefore described to be adopted, very large evolute cams would be necessary). In such case, the pinor roller-carrying rod may conveniently, but not of necessity, lie approximately in the plane of the contact surface. It may be necessary to provide means for moving the pin or roller with respect to the rod to keep it in the plane of the contact surface, as the pad wears.

In place of cam means, it is also contemplated for a rod or bar attached to the grinding or polishing pad, or its support, to slide with respect to a connecting rod the length of which, and the length of the crank of which, are adjustable.

Though mention has so far only been made to the employment of a single grinding or polishing pad, it is within the purview of the invention to employ a plurality of such pads for simultaneous grinding or polishing, each being subjected to individual orientation control.

In forming an aspheric surface of revolution it will generally be convenient to commence with a nominally spherical surface or at least a surface having revolution. Desirably the nominally spherical or other surface of revolution should be polished, at least to some extent, in order to facilitate the use of optical tests in effecting the lining up of the specimen with its axis, for example the particular radius of the sphere which passes perpendicular to the rim, or, in the case of a lens the particular radius of the surface to be ground or polished, which passes through the centre of the other surface, coincident with the axis of mounting. Usually, it will be convenient to commence with that spherical surface which touches the desired paraboloidal or other surface at the centre and cuts it at the rim.

To enable the invention to be fully understood reference is made to the accompanying diagrammatic drawing of which Figs. 1 and 2 are elevation and plan views respectively, and Fig. 3 an en- L larged fragmentary view of a detail, for an apparatus arranged in accordance with the invention for use in providing lenses with aspheric surfaces of figure of revolution.

The lens which is to be formed with a surface of prescribed figure of revolution is indicated at I as being seated in a cell 2 which is mounted on a hollow spindle 3 journalled in bearing 4 for rotation without shake, wobble or nutation precession about a vertical axis. Pivotally mounted above spindle 3 for rotation about a horizontal axis is a bar 5 to the underside of which is fastened the grinding or polishing pad 6 so that its centre lies substantially in alignment with the pivotal axis of bar 5. The pivots for the bar 5 are carried on a floating pair of links 8 pivoted at 9 to a carriage l which is guided in-slides II for horizontal movement on traverse table l2.

The carriage Ill may be arranged for reciprocation in an convenient manner but preferably under continuous control as regards the mean position of the reciprocatory traverse and in some cases as regards its amplitude. In the embodiment illustrated, link I pivoted at It to the carriage l0 carries pin I! which engages in arcuate groove I8a in lever H3, said pin i? being releasably locked in any desired position in said groove, for example by means of a butterfly wing nut I la. At one end said lever 18 is pivoted to a link [9 which is coupled with crank 20 attached to shaft 2|. Adjacent its other end said lever I8 is pivoted at IBZ) to a bar 22 which is guided in slide 23 for horizontal movement on an extension of the traverse table l2. Attached to said bar 22 is a nut 2 riding on a screwed rod 25 which is arranged for continuous rotation by servo-motor 25. It will be appreciated that, by rotation of the shaft 2!, the lever l8 will be rocked about pivot l8b accordingly to act through link 55 for moving the carriage ID to and fro to an extent which is determined by the position of adjustment of pin l! in groove l8a. With servo-motor 2E rotating, the nut 24 and thus bar 22 and pivot lBb will be continuously advanced or retracted, according to the direction of rotation of said motor, so as to cause the mean position of said to-and-fro motion of the carriage to creep either to the left or right in the drawing according to the direction of rotation of motor 25,

The operation of the servo-motor 26 will be suitably controlled, for instance by limit switch means, so that creeping of the mean position of the reciprocatory carriage i0 is effected between preset limits.

During movement of the carriage ill as described, the pad-bar 5 will be correspond ngly moved, namely to carry the grinding or polishing pad 6 over the surface of the lens in a succession of reciprocatory sweeps whose mean position is being continuously varied, for instance movin outwardly from the axis to the rim of the lens I or vice versa.

The grinding or polishing pad 6 is of construction hereinbefore referred to; as regards its size it may be mentioned by way of example that for the lens I being required to have an aspheric surface approximately paraboloidal and of paraxial radius of curvature 3.2 cm. convex and of overall diameter 6.4 cm., polishing pads ranging from 3 mm. x 5 mm. to 6 mm, x 10 mm. are contemplated.

The pad 6 is intended to bear resiliently against the surface of the lens 5 being operated upon and this may be effected under gravity but preferably is assisted by the action of spring 28 attached at one end to carriage it while its other end bears against a lug 5a projecting transversely from the pad-bar 5 to which said lug is fast.

Rigidly connected to the pad-bar 5 is a rod 29 herein referred to as the normal rod, being nominally perpendicular to the tangent plane at the centre of that surface of the pad 5 which is adapted to contact with the lens i. For engagement by the normal rod 29 is a cam 3% having shaped surface Slla whose profile is the evolute of the prescribed surface to-be formed on the lens 1. Said cam 30 is provided with universal mounting 3!, namely, to enable horizontal and vertical adjustment of said cam. It is essential that the normal rod 29 be attached to the pad-bar 5 so that the location of engagement with the cam surface 30a is coplanar with the pivotal axis of the pad-bar 5. Advantageously the normal rod 29 is resiliently urged into engagement with the cam surface 390. by means of spring 29a secured at one end to pad-bar 5 while its other end is wrapped around one of said links 8. It will be appreciated that during reciprocation of the pad 6 over the surface of lens l the normal rod 29 will roll along the cam surface 30a. Preferably the cusp of the evolute cam 38 will be adjusted to lie below the surface of the lens I by a distance equal to the specified paraxial radius for the prescribed surface of revolution to be formed. With this arrangement the grinding or polishing pad a arree 5. 11813". always substantially" the; orientation which. itwould need were; it to contact the nominal sur-- faceto beshaped, at'whatever location the move--,

ment. of the traverse carriage Ill may hav brought it to; It, will generally-suihceto arrangefor the pad 6 to he. traversed only just. beyond the pole of the surface to be shaped, duringwhich tim the normalrod 29 will pivot about the; cusp, thisbeing nominally correctfcr thezspherical surface: andv sufliciently' near: to. the. pole to be approximately correct. for: the aspheric; surface;

In using the apparatus arranged as: just describ.ed,.f'or shaping: a lens II of paraholoidal surface from fine. ground spherical form, the pad 6 will preferably beset at. about. 701%;- of the; radius; since the largest height of glassmustlbe removed from the zone. The motion of thertraverse ing carriage Iii will be adjusted to provide a traverse of /2 cm. for a pad 6 having. a contact surface which is initially plane and is. ct about. 1 cm; square. The spindle 3 supporting: thexlensl and. the shaft 2.! for effecting reciprocation. of the carriage Id are conveniently rotated from any suitable means preferably to aiford slightly more than three complete reciprocations oi the carriage for each revolution of the lens. To enable the zone to be ground to be clearly seen amultiplicity of radial lines should be penciled' on the lens 1-. In a specific case the area of effective contactbetween the pad 6 and lens I wasvinitially much; smaller than the pad and moved with respect to the pad during the traverse of the latter owing to the great height at the true figure of the 70% zone; soon the contact area had extended over most of the pad 8 while this was in mid traverse, but towards the extremities of the traverse more than half of the pad was notcontacting' the lens at all, being manifest by the nonremoval of the pencil lines; the machine could safely be left operating until thepencillines had vanished up to the limit of the traverse; wher upon the traverse was increased, forinstance-by adjustment of the position of the pin H in the a groove mo. Most of the grinding was efi'ecte'd with slightly more than three complete traverse strokes for each revolution of the lens; and padbreadths of from 5 to 6 mm. with creeping rates of from 0.61 to 0.1 mm. radially per traverse stroke.

Advisably, optical tests, for example the Fou cault knife-edge test, should be applied at frequent intervals during grinding or polishing and the pad traverse stroke and creeping limits accordingly adjusted without removing the specimen from the spindle. For this purpose theremay conveniently be provided within the cell 2 in which the lens I is seated, a screen 32 formed with a pin-hole 32a, and a lens 33 suitably mounted coaxially with said lens i by means of tube 36 in which said lens is seated and which is secured to said screen 32; the light beam for carrying out the test being arranged to be pro jected through the hollow' spindle 3 on to thelens 33'.

The: apparatus is: applicable either in the: for-- mation of concave or convex; surfaces; It will generally be round to conduce to faster grinding if: the grinding or polishing pad is loaded so that the centre of pressure is nearer to the trailing than the leading edge.

Although in making lenses and the like th prescribed shape will usually be of revolution about the axis of a. conic or similar curve, the ins vention may also beused to makeother shapes: of. revolution, for-example, a portion. of a. conic, including the pole, rotated about a lineperpen-- dicular to its major axis. Such shapes may be; convenient asgauges in work'with aspheric lenses (for example a profile gauge consisting of a hyperboloid of one sheet, to test a convex: lens which is one sheet of a hyperboloid of two: sheets).

What'I claim, as new and desire to secure by Letters Patent. of the. United States is:

1. Apparatus for grinding and/or polishing: a lens to'form thereon an asphericv surface of prescribed fi'gure of revolution, comprising means for mounting the lensfor rotation about a fixedvertical axis, a bar pivoted about" a horizontal axis to a carriage which is arranged for horizontal reciprocation towards and away from the said vertical axis, a grinding or polishing pad secured to the underside of the said bar and arranged for presenting a grinding or polishing surface to the lens which is small, for example 5% or less, in relation to the surface of prescribed figure,

and which surface is yieldingly engaged with thelens, a rod or bar secured to the bar carrying saidgrinding or polishing pad so as to extend substantially normally to the grinding or polishing surface, and a cam presenting a surface along which said rod or bar is adapted to roll during reciprocation of the carriage, which cam. surface is in profile the evolute of the surface of prescribed figure of revolution.

2: Apparatus as defined in claim 1', including means for adjusting the mean position of reciprocation ofxsaid grinding. or polishing surface. relatively to the axis of rotation of said lens.

CECIL REGINALD BURCH.

REFERENCES CITED The following references. are of record in the file of this; atent:

UNITED STATES PATENTS Number Name Date Re.13,7'0.6 Beam l Mar. 3-1',v 19.1% 547,132, Clark Octl 1,1895- 995 3%. Witmer June 13, 19111 FOREIGN PATENTS Number Country Date:

3,3514. Great. Britain Mar. 2', 19.15- 'l .5.2f7- Great Britain Feb. 23, 19.07: 

